Comparative Analysis of Stress Distribution through Finite-Element Models of 3 NiTi Endodontic Instruments while Operating in Different Canal Types

Statement of the Problem: Distribution of stress along endodontic instruments determines their fracture resistance during instrumentation of root canals. The cross-sectional design of instruments and root canal anatomy are of the most important factors affecting the stress distribution. Purpose: The purpose of this study was to evaluate the stress distribution in different cross-sectional design of nickel-titanium (NiTi) endodontic instruments operating in different canal anatomies using finite element analysis (FEA). Materials and Method: In this original finite element analysis study, 3-dimensional models of convex triangle (CT), S-type (S), and triple-helix (TH) cross-sectional designs with the size of 25/04 simulated rotational movements through 45ᵒ and 60ᵒ angled root canals with 2- and 5-mm radii using ABAQUS software. The stress distribution was evaluated by the means of FEA. Results: CT showed the lowest stress values followed by the TH and S ones. The most stress concentration was detected in the CT apical third while, TH revealed better stress distribution all along its length. 45ᵒ curvature angle and 5-mm radius applied the lowest stress to the instruments. Conclusion: Higher value of radius and smaller curvature angle apply lower stress values to the instrument. CT design shows the lowest stress level with the most stress concentration in its apical third while the triple-helix design has a better stress distribution. Thus, it is safer to use convex triangular cross-section mostly for coronal and middle thirds in initial steps of shaping and triple-helix for the apical third in final steps.


Introduction
Nickel-titanium (NiTi) rotary instruments have been introduced in 1990s and since then, they have brought root canal instrumentation more effectiveness and speed [1] and also reduced risk of transportation because of their excellent flexibility [2]. However, despite many advantages, intracanal separation still occurs with any rotary instrument that can lower the prognosis of the endodontic treatment by leaving the infectious tissue apical to the fractured segment [3]. Instrument separation is due to two main factors. The first factor is the cyclic fatigue caused by reappearance of bending stresses in curved canals. The second factor is torsion produced within the rotary file when it is blocked against the canal wall, or proposed to disproportionate pressure by the operator [1]. As the ease of application and effectiveness of rotary instrumentation have increased, its employment by general and other dental practitioners has increased; hence, the intracanal separation has become a matter of concern [4].
Many studies have been carried out to find the most fracture resistant rotary system and the reasons causing fractures [5][6][7] and have reported that the design and the manufacturing processes are the main factors determining the mechanical performance of NiTi instruments.
There are various rotary systems available in the market with different cross-sectional geometries and still, there is scarce evidence proving which cross-section is more appropriate for which root canal anatomy. Some studies have evaluated cyclic fatigue resistance of endodontic instruments by traditional experimental approaches [8][9][10][11]. However, the mechanical behavior of rotary instruments can also be analyzed by finite element analysis (FEA), a numerical method to analyze the stress distribution and concentration in NiTi rotary instruments, which are impossible to be evaluated during actual instrumentation [1].
The purpose of the present study was to evaluate the stress distribution of three rotary instruments with dif- The mechanical characteristics of NiTi alloy and dentin component of the root canal were setting as: Young's modulus 36 GPa, the Passion's ratio 0.30, the stress range for austenite to martensite phase transformation 504-600 MPa for the NiTi alloy [12] and the Young's modulus 18.60 and the Poisson's ratio 0.30 for dentin [2].
The accumulation of plastic deformation due to cyclic loading in the pseudo-elastic range and the shear strains due to friction of the instrument blade into the canal wall were neglected as model simplifications. Figure 3 shows the stress distribution in three instruments while rotating in simulated canals in a longitudinal inner view and Table 1

Discussion
This study evaluated the stress distribution and stress concentration in three different rotary instruments. Examination of fractures at high magnification reveals the crack origin and the mode of material failure [13].
However, it cannot estimate the stress distribution on the instrument that might contribute to its breakage. It is also impossible to evaluate the stresses distributed along the instrument during its actual clinical use. Therefore, a computerized simulation can be useful. In medical and dental research, FEA has been widely used to analyze the stress distribution in complex structures for years [14]. So, as many other studies [1][2]12,15], we evaluated the stress distribution along three different endodontic instruments by the means of FEA. Several studies have reported the cross-section profile as the main factor for NiTi instruments torsional behavior [5][6][7]. In the present study, we regenerated computerized models with different geometries but the same size and taper in different boundary conditions (simulated curved canals) concerning the material mechanical properties. There is no information about "fit" of the instrument in the simulated canals in most articles and some have described the canal diameter wider than the file [5,16]. As the instrument is likely to be fitting loosely in canals, the description of the radius in these studies may be overstated and the file was bent less severely than reported.
In addition, most previous studies have not considered the canal taper [16][17][18] larger inner core to spread the stress but larger inner core results in less flexibility that requires higher loads to bend. This can increase the stress level in the apical section, which is more bent. Accumulation of maximum stress in the apical third of the CT design increases the risk of its fracture and it is safer to use it for coronal and middle thirds shaping.

Conclusion
Higher value of radius and smaller curvature angle apply lower stress values to the instrument. In this study, 5-mm of radius and 45 ᵒ curvature angle was the best operating condition while 2-mm radius and 60 ᵒ angle was the worst. Convex triangle design showed the lowest stress level compared with triple-helix and S-type cross sections. Convex triangle design showed the most stress concentration in its apical third while the triplehelix design had a better stress distribution. Thus, it is safer to use convex triangular cross-section mostly for coronal and middle thirds in initial steps of shaping and triple-helix for the apical third in final steps.